Correlation energy of two electrons in a ball

Abstract

We study the ground-statecorrelationenergyEc of two electrons of opposite spin confined within a D-dimensional ball (D≥2) of radius R. In the high-density regime, we report accurate results for the exact and restricted Hartree–Fock energy, using a Hylleraas-type expansion for the former and a simple polynomial basis set for the latter. By investigating the exact limiting correlationenergyEc⁽⁰⁾=limR→0Ec for various values of D, we test our recent conjecture [P.-F. Loos and P. M. W. Gill, J. Chem. Phys.131, 241101 (2009)] that in the large-D limit, Ec⁽⁰⁾∼−δ2/8 for any spherically symmetric confining external potential, where δ=1/(D−1). Show more